kichimark
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On the flip side, perhaps the polyp does not feed while it is splitting. It strictly uses photosythesis for its energy untill reproduction has ended.
THIS.
I would assume during these times that the zooxanthallae which the coral utilizes would contribute the most to the energetic needs of the polyps since their mouths are still forming/healing.
I would also hypothesize that IF the original polyp were to eat while the newer one doesn't that the newer polyp from the split may still be putting the final touches on its development and may not be as well developed of the "mother".